Page 128 - Start Up Mathematics_7

Proportion
The equality of two ratios is called proportion. The numbers a, b, c and d are in proportion if the
ratio of a and b is equal to the ratio of c and d, i.e., a : b = c : d. We can also use the symbol ‘: :’
for proportion. The numbers a and d are known as extremes and b and c are known as means.
For a, b, c and d to be in proportion, the product of extremes is equal to the product of means,
i.e., a × d = b × c.
Example 1: Find the ratio of:
(a) ` 5 to 50 paise (b) 15 kg to 2,100 g (c) 20 days to 72 hours
Solution: We first convert the quantities so that they are in same units.
(a) ` 5 = 500 paise
∴ the ratio, ` 5 : 50 paise is 500 : 50 = 10 : 1
(b) 15 kg = 15,000 g
∴ the ratio, 15 kg : 2,100 g = 15,000 : 2,100 = 50 : 7
(c) 20 days = 20 × 24 hours = 480 hours
∴ the ratio, 20 days : 72 hours = 480 : 72 = 20 : 3
Example 2: In a computer lab, there are 4 computers for every 6 students. How many computers
will be needed for 36 students?

Solution: Let the number of computers needed be x.
Then, 4 : 6 = x : 36
4 x
⇒ =
6 36
4 × 36
⇒ x = = 24 computers
6
Example 3: Population of Rajasthan = 570 lakhs and population of UP = 1,660 lakhs
2
Area of Rajasthan = 3 lakh km and area of UP = 2 lakh km 2
2
(a) How many people are there per km in both these states?
(b) Which state is less populated? (NCERT)
Solution: (a) (i) Population of Rajasthan = 570 lakh

Area of Rajasthan = 3 lakh km 2
2
∴ Number of people per km = 570 lakh = 190 people
3 lakh
(ii) Population of UP = 1,660 lakh
Area of UP = 2 lakh km 2
1,660 lakh
2
∴ Number of people per km = 2 lakh = 830 people
(b) Rajasthan is less populated.

Percentage
It is another method of comparing quantities. In this method, we find out of hundred. In fact
percent is derived from Latin word ‘per centum’ which means ‘per hundred’. It is represented
by the symbol %. It also means hundredths. For example, 5% means 5 out of hundred. It can be
written as:

5% = 5 = 0.05
100

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